Present and future communication systems take more and more advantage of the spatial properties of the MIMO radio channel. Such radio channels are established by using multiple antennas at either end of the communication link, for example at a base station and a mobile station.
In a point to multipoint communication system, as for instance the downlink of a mobile communication system, the transmitter has the important task of assigning resources such as time, frequency and space components to the receivers under its coverage. If the transmitter knows the channel of each user, multiple users can be served at the same time and over the same frequency multiplexing them in space. In a multipoint to point communication system, as for example the uplink of a mobile communication system, this task has to be accomplished by the receiver. In the following the analysis will illuminate the downlink, application to the uplink is straightforward. For this purpose multiple antennas at the base station or access point and at the mobile users are employed, which leads to the well-known MIMO systems. Here, a MIMO system with K users with MTx antennas at the transmitter and MRx,k antennas at the k-th receiver is considered. The k-th user's channel is described by the matrixHkε℄MRx,k×MTx.
In the literature a lot of algorithms can be found which perform a resource allocation based on instantaneous knowledge of all matrices Hk at the transmitter. To name only a few, there are Block Diagonalization (BD=Block Diagonalization) as described by Q. H. Spencer, A. L. Swindlehurst, and M. Haardt in Zero-forcing Methods for Downlink Spatial Multiplexing in Multiuser MIMO Channels, IEEE Trans. on Signal Processing, 52:461-471, 2004, Orthogonal Frequency Division Multiple Access (OFDMA=Orthogonal Frequency Division Multiple Access) as described by K. Seong, M. Mohseni, and J. M. Cioffi in Optimal Resource Allocation for OFDMA Downlink Systems, In Proc. of International Symposium of Information theory (ISIT), 2006 and the Successive Encoding Successive Allocation Method (SESAM=Successive Encoding Successive Allocation Method) as described by P. Tejera, W. Utschick, G. Bauch, and J. A. Nossek in Subchannel Allocation in Multiuser Multiple Input Multiple Output Systems, IEEE Transactions on Information Theory, 52:4721-4733, October 2006.
These algorithms necessitate full channel state information (CSI=Channel State Information) at the transmitter. In Time Division Duplex (TDD=Time Division Duplex) systems this necessitates the estimation of MTxMRx,k coefficients per channel realization for each user at the transmitter. In Frequency Division Duplex (FDD=Frequency Division Duplex) systems, where unlike in TDD systems, the reciprocity of uplink and downlink cannot be exploited straightforwardly, these complex coefficients need to be fed back from the mobile receivers to the base station. Furthermore the dimensions of the matrices Hk determine the computational complexity of these transmit signal processing algorithms, as they are based on Singular Value Decompositions (SVD=Singular Value Decomposition) of these matrices.
The SESAM algorithm is shortly reviewed here as an exemplified concept. The algorithm works as follows:
First the principal singular value of each user σk,i,1 is determined, whereby i denotes the dimension index and the index 1 stands for the principal singular value. Currently i=1.
Afterwards the user with the largest singular value
      σ                  π        ⁡                  (          1          )                    ,      1      ,      1        =            max      k        ⁢          σ              k        ,        1        ,        1            is selected for transmission in the first spatial domain. π(i) thereby denotes the encoding order function, i.e. π(1) refers to the user encoded in dimension 1. The transmit beamforming vector is given by the left singular vector υ1 corresponding to the principal singular value of user π(1).
To determine the user in the second dimension first all channels are projected into the null space of υ1, such that the following users do not interfere with user π(1). The projected channels Hk,2 are obtained by the matrix operationHk,2=Hk(IMTx−υ1υ1H)  (1.1)wherein IMTx denotes the MTx×MTx identity matrix and the second index of the channel matrix constitutes the dimension index.
Note that this operation only guarantees that user π(2) does not interfere with user π(1). Interference from user π(1) to user π(2) is canceled by means of Dirty Paper Coding (DPC) as described by Max H. M. Costa, Writing on Dirty Paper, IEEE Transactions on Information Theory, 29:439-441, May 1983. User selection is now performed with the projected channels and the user with the maximum projected singular value is chosen for transmission. The corresponding transmit vector υ2 is the principal right singular vector of the projected channel matrix Hπ(2),2. The process is continued by further projecting the matrices Hk,2 into the nullspace of υ2 and selecting the user for the next spatial dimension until no spatial dimension is left. By this procedure up to MTx scalar sub channels are generated. As on each sub channel no interference occurs, the optimum power allocation is determined by water filling over the sub channels. The SESAM algorithm can be easily extended to Orthogonal Frequency Division Multiplexing (OFDM=Orthogonal Frequency Division Multiplexing) systems by decomposing the MIMO channels into scalar sub channels on each sub carrier separately as described above and performing water filling over the sub channels of all carriers.